Unfortunately it won't be a good hum-cancelling arrangement. The PB pickup is already hum cancelling - one of the split coils is reverse wound & reverse polarity to the other split coil. So the output is (in theory) already hum free. If you change the polarity of one of the split coils, then you get the hum back, plus a small amount of phase cancellation on the A and D strings. But unless the JB pickup has a similar coil configuration (which it doesn't), the levels of hum are likely to be different and so partial hum cancellation is the best you can hope for. The JB pickup would also have to be out of phase with one of the PB split coils, so you'll end up with a thin nasal sound on two strings, a normal parallel sound on the other two strings, plus some hum.
I think it would be better to concentrate on shielding the cavities to reduce the level of hum, and go with something like the Entwhistle Neo, and then look round on eBay for a used noiseless JB pickup if hum is an issue. A few years ago I managed to pick up a used set of Bartolini noiseless JB pickups to replace a very noisy single coil set in a Yamaha BB604 for about A$60.